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math.DS2026
On the Julia sets of the non-autonomous iteration of exponential maps
Jiaxing Huang, Xiao Yao
This paper studies non-autonomous iterations of , where at each step the parameter is chosen from a bounded interval. Urbański and Zdunik introduced and developed a therm…
math.DS2026
Non-analyticity of hairs of exponential maps
Weiwei Cui, Jiaxing Huang, Lingrui Wang
Let , where . In 1984, Devaney and Krych showed that the Julia set consists of pairwise disjoint hairs. Viana further in 1988 proved that these hairs are $C^{…
math.DS2026
Dynamical (non-)recurrence of escaping exponential maps
Weiwei Cui, Jiaxing Huang, Jun Wang
We show that exponential maps could have complicated measurable behaviours by giving two examples in the exponential family both with singular value escaping to infinity ``slowly",…